Anybody have some major pro tips for someone starting to go to the gym regularly?
It depends on what your goals are, but it's good to do a mix of strength/resistance training, along with cardio get-your-heart-rate-up training. I personally do 6 days a week (3 days a week of each), around 90 minutes per day. That typically works out to 60-75 minutes of actual lifting or actual cardio, then 15-30 minutes of abs/core + stretching.
As several people have said, start out moderately, then increase the intensity and duration of the workouts. You're probably in for a tough/sore few weeks at the outset, but don't let that discourage you. It won't feel like it for a couple dozen days, but your body will in fact adapt.
Your body will get used to the new workouts, and it'll get much, much better in month 2. Then, you'll take off in terms of weight improvement, strength, endurance, etc. As you begin to work your muscles in ways you haven't before, it's good to get into the habit of regularly stretching. I know there are a number of theories on this front, but I'm not a fan of stretching cold muscles, so I always stretch at the end of my workout.
Most gyms have bootcamp-type workouts that I think are awesome. They're usually a mix of strength-cardio, and I find that when I use machines, I simply cannot get my heartrate up as high as those classes get it, short of running the steps at Red Rocks or something. The treadmills and stairmasters are fine and all, but there are better ways to get an awesome cardio workout in. Getting your heartrate up a few times a week is important.
As others have said, don't be shy about asking questions of those in the gym who obviously know what they're doing. Most people are willing to help.
Finally, take the long view. A lot of people join a gym and start working out, thinking that they're going to get easy/immediate results in a week or two or something. If you dedicate yourself to it for 6 months, you'll absolutely feel the difference, and quite likely see it as well.